Finite Group DatabasebetaFinite Group Databasebeta| order | 1375 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C125 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊C125 |
| derived, Sylow | C11 ⋊ C125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C25 | C11⋊C5 |
| commutator, hypocenter | C11 | C125 |
| Fitting, cosocle | C11×C25 | C5 |
| socle, prime radical | C5×C11 | C25 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C25 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 136 |
| transitive degree | μt(G) = 1375 |
Polycyclic presentation:
5^3,11|a^5=b,b^5=c,d^a=d^4175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1375, 6);